## Pseudo arc-length continuation method for multiple solutions in one-dimensional steady state semiconductor device simulation

 dc.contributor.advisor Roger K. Alexander dc.contributor.author Tso, Tai-Yih dc.contributor.department Mathematics dc.date 2018-08-16T07:17:59.000 dc.date.accessioned 2020-06-30T07:01:50Z dc.date.available 2020-06-30T07:01:50Z dc.date.copyright Tue Jan 01 00:00:00 UTC 1991 dc.date.issued 1991 dc.description.abstract

This dissertation is concerned with numerical simulation and study of the multiple steady states for a three junction semiconductor device. The semiconductor device is modeled by the drift-diffusion equations formulated by Van Roosbroeck. These nonlinear differential equations, the Poisson equation, two continuity equations and two current equations, describe the potential distribution, carrier concentration, and current flow within semiconductor devices;The system of semiconductor device equations can not be solved explicitly in general. The finite difference box method is used to transform the continuous equations into nonlinear algebraic system. The solutions are computed by two iterative schemes: Gummel's method and Newton's method;The basic goal in this dissertation is numerical simulation of one-dimensional steady state thyristors. A thyristor is a semiconductor device with four layer structure, used to control the switching of dc and ac power. Numerical simulation of thyristors is quite difficult because they have multiple steady states. The snap-back phenomenon in the current-voltage characteristic of thyristors has caused computational problems. We applied the arc-length continuation method to overcome the snap-back and multi-solution problems. We successfully obtain the current-voltage characteristic of thyristors by this method.

dc.format.mimetype application/pdf dc.identifier archive/lib.dr.iastate.edu/rtd/10078/ dc.identifier.articleid 11077 dc.identifier.contextkey 6385042 dc.identifier.doi https://doi.org/10.31274/rtd-180813-9519 dc.identifier.s3bucket isulib-bepress-aws-west dc.identifier.submissionpath rtd/10078 dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/63184 dc.language.iso en dc.source.bitstream archive/lib.dr.iastate.edu/rtd/10078/r_9202399.pdf|||Fri Jan 14 18:13:01 UTC 2022 dc.subject.disciplines Electrical and Computer Engineering dc.subject.disciplines Mathematics dc.subject.keywords Mathematics dc.title Pseudo arc-length continuation method for multiple solutions in one-dimensional steady state semiconductor device simulation dc.type article dc.type.genre dissertation dspace.entity.type Publication relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 thesis.degree.level dissertation thesis.degree.name Doctor of Philosophy
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